I'm not 100% sure, but wave function collapse might involve some non-linearity somewhere, whichight also be detectable in some fashion.
On the other hand, Bohm's interpretation seems pretty ad hoc. And it also includes all of the other worlds that MWI has in it via the pilot waves that continue to exist and propagate forever. (The pilot waves never collapse.) It's just that only one of those many worlds ends up being "real".
Necessarily, this lesser infinity of universes would tend to be extremely similar, and would average out to some kind of consensual reality, with the variation noise only becoming evident if one looked very closely (superposition, casimir effect, uncertainty principle, etc)
So the act of observation would merely divide this lesser infinity into two lesser infinities which would be distinct unless they were reunited by a reverse-time coherence such as many quantum experiments have demonstrated.
I would suspect that statistically, such reverse-time coherences are pretty common inside of one's personal light cone, so in this respect, I would guess that the "universe bandwidth" is probably quite robust and requires a pretty significant (macroscopic scale) effect in order to divide permanently into distinct infinities for a given observer.
Of course this is all just metaphysical conjecture, but Id be interested if anyone is seriously thinking along similar lines.